improving deep neural networks notes

Be able to implement and apply a variety of optimization algorithms, such as mini-batch gradient descent, Momentum, RMSprop and Adam, and check for their convergence. gamma and beta are learnable parameters of the model. This is the second course of the deep learning specialization at Coursera which is moderated by Multiple Neural Networks Another simple way to improve generalization, especially when caused by noisy data or a small dataset, is to train multiple neural networks and average their outputs. In practice most often you will use a deep learning framework and it will contain some default implementation of doing such a thing. L2-regularization relies on the assumption that a model with small weights is simpler than a model with large weights. In five courses, you will learn the foundations of Deep Learning, understand how to build neural networks, and learn how to lead successful machine learning projects. In practice people don't bother implementing. If you have enough computational resources, you can run some models in parallel and at the end of the day(s) you check the results. Neural Networks (NNs) also known as Artificial Neural Networks (ANNs),Connectionist Models, and Parallel Distributed Processing (PDP) Models 2. In the present review, we relate continual learning to the learning dynamics of neural networks, highlighting the potential it has to considerably improve data efficiency. Vector d[l] is used for forward and back propagation and is the same for them, but it is different for each iteration (pass) or training example. Course Notes. When we train a NN with Batch normalization, we compute the mean and the variance of the mini-batch. We need another dat… Deep Learning Specialization Overview 2. because 50 million won't fit in the memory at once we need other processing to make such a thing. Hyperparameter tuning, Batch Normalization, Programming ... 6395 reviews. For instance, here 10 neural networks are trained on a small problem and their mean squared errors compared to the means squared error of their average. Learn more. Course 2: Improving Deep Neural Networks: Hyperparameter tuning, Regularization and Optimization. ${1_{st}}$ week: practical-aspects-of-deep-learning, $3_{rd}$ week: hyperparameter-tuning-batch-normalization-and-programming-frameworks, week1: practical-aspects-of-deep-learningweek2: optimization-algorithmsweek3: hyperparameter-tuning-batch-normalization-and-programming-frameworks, Improving Deep Neural Networks: Hyperparameter tuning, Regularization and Optimization, 01_setting-up-your-machine-learning-application, 02_why-regularization-reduces-overfitting, 03_weight-initialization-for-deep-networks, 06_gradient-checking-implementation-notes, 02_understanding-mini-batch-gradient-descent, 04_understanding-exponentially-weighted-averages, 05_bias-correction-in-exponentially-weighted-averages, hyperparameter-tuning-batch-normalization-and-programming-frameworks, 02_using-an-appropriate-scale-to-pick-hyperparameters, 03_hyperparameters-tuning-in-practice-pandas-vs-caviar, 02_fitting-batch-norm-into-a-neural-network, 04_introduction-to-programming-frameworks, Improving the Robustness of Deep Neural Networks via Stability Training Abstract: In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. To understand how they work, you can refer to my previous posts. We need to tune our hyperparameters to get the best out of them. In the previous video, the intuition was that dropout randomly knocks out units in your network. In the last layer we will have to activate the Softmax activation function instead of the sigmoid activation. 0.10%. We can use the weighted average across the mini-batches. Suppose we have m = 50 million. If λ is too large, it is also possible to "oversmooth", resulting in a model with high bias. This is the second course of the Deep Learning Specialization. Another idea to get the bias / variance if you don't have a 2D plotting mechanism: high Bias (underfitting) && High variance (overfitting) for example: These Assumptions came from that human has 0% error. Like the course I just released on Hidden Markov Models, Recurrent Neural Networks are all about learning sequences – but whereas Markov Models are limited by the Markov assumption, Recurrent Neural Networks are not – and as a result, they are more expressive, and more powerful than anything we’ve seen on tasks that we haven’t made progress on in decades. The course is taught by Andrew Ng. Your data will be split into three parts: Training set. Specifically, the overall reduction in epochs was 13.67%. so the trend on the ratio of splitting the models: If size of the dataset is 100 to 1000000 ==> 60/20/20, If size of the dataset is 1000000 to INF ==> 98/1/1 or 99.5/0.25/0.25. It depends a lot on your problem. In this section we will learn the basic structure of TensorFlow programs. With such a deep neural network, if your activations or gradients increase or decrease exponentially as a function of L, then these values could get really big or really small. As was presented in the neural networks tutorial, we always split our available data into at least a training and a test set. and the copyright belongs to Improving Deep Neural Networks Posted on 2019-04-20 | Edited on 2019-04-24 ... Specialization. Implementation tip: if you implement gradient descent, one of the steps to debug gradient descent is to plot the cost function J as a function of the number of iterations of gradient descent and you want to see that the cost function J decreases monotonically after every elevation of gradient descent with regularization. Programming frameworks can not only shorten your coding time but sometimes also perform optimizations that speed up your code. Rather than the deep learning process being a black box, you will understand what drives performance, and be able to more systematically get good results. 4 stars. The mean and the variance of one example won't make sense. Code v.2 (we feed the inputs to the algorithm through coefficients): We use optional third-party analytics cookies to understand how you use so we can build better products. The result should be w = 5 as the function is (w-5)^2 = 0. Training a bigger neural network never hurts. A lot of researchers are using dropout with Computer Vision (CV) because they have a very big input size and almost never have enough data, so overfitting is the usual problem. In Batch gradient descent we run the gradient descent on the whole dataset. 10.56%. It becomes too costly for the cost to have large weights! L2 regularization is being used much more often. You signed in with another tab or window. Batch normalization does some regularization: Each mini batch is scaled by the mean/variance computed of that mini-batch. In mini-batch algorithm, the cost won't go down with each step as it does in batch algorithm. To solve the bias issue we have to use this equation: The momentum algorithm almost always works faster than standard gradient descent. Don't use the gradient checking algorithm at training time because it's very slow. A better terminology is to call it a dev set as its used in the development. You will also learn TensorFlow. And each day you nudge your parameters a little during training. layers; Hidden units; Learning rates ; Activation functions; Idea - Code - Experiment. We have to compute an estimated value of mean and variance to use it in testing time. This leads to a smoother model in which the output changes more slowly as the input changes. Softmax is a generalization of logistic activation function to C classes. Thus, by penalizing the square values of the weights in the cost function you drive all the weights to smaller values. It will take a long time for gradient descent to learn anything. This is my personal summary after studying the course, Improving Deep Neural Networks: Hyperparameter tuning, Regularization and Optimization, which belongs to Deep Learning Specialization. In this set of notes, we give an overview of neural networks, discuss vectorization and discuss training neural networks with backpropagation. Now lets compute the Exponentially weighted averages: If we plot this it will represent averages over, Best beta average for our case is between 0.9 and 0.98. It's possible to show that dropout has a similar effect to L2 regularization. It has to be a power of 2 (because of the way computer memory is layed out and accessed, sometimes your code runs faster if your mini-batch size is a power of 2): Make sure that mini-batch fits in CPU/GPU memory. With such a deep neural network, if your activations or gradients increase or decrease exponentially as a function of L, then these values could get really big or really small. But a lot of people in this case call the dev set as the test set. Here are some of the leading deep learning frameworks: These frameworks are getting better month by month. Discussion and Review In this paper, we propose a new approach for improving accuracy of traffic sign recognition. You will also learn TensorFlow. If we are using batch normalization parameters b[1], ..., b[L] doesn't count because they will be eliminated after mean subtraction step, so: So if you are using batch normalization, you can remove b[l] or make it always zero. And this makes training difficult, especially if your gradients are exponentially smaller than L, then gradient descent will take tiny little steps. Plateau is a region where the derivative is close to zero for a long time. L2 matrix norm because of arcane technical math reasons is called Frobenius norm: The normal cost function that we want to minimize is: 1 Neural Networks We will start small and slowly build up a neural network, step by step. The input layer dropout has to be near 1 (or 1 - no dropout) because you don't want to eliminate a lot of features. J(w,b) = (1/m) * Sum(L(y(i),y'(i))) + (lambda/2m) * Sum((||W[l]||^2), We stack the matrix as one vector (mn,1) and then we apply sqrt(w1^2 + w2^2.....), To do back propagation (old way): Improving the Interpretability of Deep Neural Networks with Knowledge Distillation Xuan Liu , Xiaoguang Wangy, Stan Matwinz Institute for Big Data Analytics Faculty of Computer Science, Dalhousie University, Halifax, NS, Canada Email: yAlibaba Group, Hangzhou, China Email: zInstitute of Computer Science Polish Academy of Sciences, … Our numpy implementations were to know how NN works. In the rise of deep learning, one of the most important ideas has been an algorithm called. Don't use dropout (randomly eliminate nodes) during test time. You will learn about Convolutional networks, RNNs, LSTM, Adam, Dropout, BatchNorm, Xavier/He initialization, and more. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. Before we normalized input by subtracting the mean and dividing by variance. We will pick the point at which the training set error and dev set error are best (lowest training cost with lowest dev cost). DOI: 10.1109/ICCP51029.2020.9266162 Corpus ID: 227232667. For example in OCR, you can impose random rotations and distortions to digits/letters. Implications of L2-regularization on: Training NN with a large data is slow. However, most existing methods dedicate to developing more sophisticated attention modules for achieving better performance, which inevitably increase model complexity. This method is also sometimes called "Running average". Rather than the deep learning process being a black box, you will understand what drives performance, and be able to more systematically get good results. Different (advanced) optimization algorithms. 1 star. This makes your inputs centered around 0. You will try to build a model upon training set then try to optimize hyperparameters on dev set as much as possible. So If W > I (Identity matrix) the activation and gradients will explode. The bias correction helps make the exponentially weighted averages more accurate. You could also apply a random position and rotation to an image to get more data. Symmetry is still broken so long as $W^{[l]}$ is initialized randomly, Different initializations lead to different results, Random initialization is used to break symmetry and make sure different hidden units can learn different things, Don't intialize to values that are too large. And If W < I (Identity matrix) the activation and gradients will vanish. If algorithm fails grad check, look at components to try to identify the bug. One of the ways to tune is to sample a grid with. Convolutional Neural Networks Course Breakdown 3. The Vanishing / Exploding gradients occurs when your derivatives become very small or very big. If you normalize your inputs this will speed up the training process a lot. Be able to implement a neural network in TensorFlow. If we don't normalize the inputs our cost function will be deep and its shape will be inconsistent (elongated) then optimizing it will take a long time. Make sure the dev and test come from the same distribution. Suppose we have split m to mini batches of size 1000. The trend now gives the training data the biggest sets. : What you should remember: To solve that you'll need to turn off dropout, set all the. Improving the Accuracy of Deep Neural Networks Through Developing New Activation Functions @article{Mercioni2020ImprovingTA, title={Improving the Accuracy of Deep Neural Networks Through Developing New Activation Functions}, author={Marina Adriana Mercioni and Angel Marcel Tat and S. Holban}, journal={2020 IEEE 16th … Don't rely on batch normalization as a regularization. When you train networks for deep learning, it is often useful to monitor the training progress. There is a partial solution that doesn't completely solve this problem but it helps a lot - careful choice of how you initialize the weights (next video). So here the explanation of Bias / Variance: If your model is underfitting (logistic regression of non linear data) it has a "high bias", If your model is overfitting then it has a "high variance", Your model will be alright if you balance the Bias / Variance. As mentioned before mini-batch gradient descent won't reach the optimum point (converge). Let's say you have a specific range for a hyperparameter from "a" to "b". We can implement this algorithm with more accurate results using a moving window. Some people are making changes to the learning rate manually. Recall the housing price prediction problem from before: given the size of the house, we want to … In programming language terms, think of it as mastering the core syntax, libraries and data structures of a new language. and the copyright belongs to You should try the previous two points until you have a low bias and low variance. It is better to make sure that dev and test set are from the same distribution. Instead of needing to write code to compute the cost function we know, we can use this line in TensorFlow : To initialize weights in NN using TensorFlow use: For 3-layer NN, it is important to note that the forward propagation stops at. too noisy regarding cost minimization (can be reduced by using smaller learning rate), won't ever converge (reach the minimum cost), make progress without waiting to process the entire training set, doesn't always exactly converge (oscelates in a very small region, but you can reduce learning rate). In testing we might need to process examples one at a time. Photo by timJ on Unsplash. If you’ve understood the core ideas well, you can rapidly understand other new material. A most common technique to implement dropout is called "Inverted dropout". For example, if. And this makes training difficult, especially if your gradients are exponentially smaller than L, then gradient descent will take tiny little steps. In deep learning frameworks there are a lot of things that you can do with one line of code like changing the optimizer. Forcing the inputs to a distribution with zero mean and variance of 1. It turns out you can make a faster algorithm to make gradient descent process some of your items even before you finish the 50 million items. Neural networks are widely used in supervised learning and reinforcement learning problems. 80% stay, 20% dropped, # increase a3 to not reduce the expected value of output, # (ensures that the expected value of a3 remains the same) - to solve the scaling problem, # can be written as this - cost = w**2 - 10*w + 25, # Runs the definition of w, if you print this it will print zero, # better for cleaning up in case of error/exception. We use essential cookies to perform essential website functions, e.g. Hold-out cross validation set / Development or "dev" set. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. if it is < 10^-7 - great, very likely the backpropagation implementation is correct, if around 10^-5 - can be OK, but need to inspect if there are no particularly big values in, if it is >= 10^-3 - bad, probably there is a bug in backpropagation implementation. dw[l] = (from back propagation) + lambda/m * w[l]. If you're more worried about some layers overfitting than others, you can set a lower. The value of λ is a hyperparameter that you can tune using a dev set. To make inputs belong to other distribution (with other mean and variance). The last example explains that the activations (and similarly derivatives) will be decreased/increased exponentially as a function of number of layers. Adding regularization to NN will help it reduce variance (overfitting). Improving their performance is as important as understanding how they work. Run the Session. He initialization works well for networks with ReLU activations. Then, if we have 2 hidden units per layer and x1 = x2 = 1, we result in: A partial solution to the Vanishing / Exploding gradients in NN is better or more careful choice of the random initialization of weights, In a single neuron (Perceptron model): Z = w1x1 + w2x2 + ... + wnxn, So it turns out that we need the variance which equals 1/n_x to be the range of W's. It's unlikely to get stuck in a bad local optima in high dimensions, it is much more likely to get to the saddle point rather to the local optima, which is not a problem. For regularization use other regularization techniques (L2 or dropout). 0.05%. IMPROVING DEEP NEURAL NETWORKS FOR LVCSR USING RECTIFIED LINEAR UNITS AND DROPOUT George E. Dahl?Tara N. Sainathy Geoffrey E. Hinton? And when it comes to image data, deep learning models, especially convolutional neural networks (CNNs), outperform almost all other models. This is where algorithms like momentum, RMSprop or Adam can help. So the parameters will be W[l], beta[l], and alpha[l]. The code inside an epoch should be vectorized. We will take these parameters as the best parameters. In most cases Andrew Ng tells that he uses the L2 regularization. For example, you can determine if and how quickly the network accuracy is improving, and whether the network is starting to overfit the training data. For example if we are classifying by classes. Deep Neural Networks are the solution to complex tasks like Natural Language Processing, Computer Vision, Speech Synthesis etc. For example if cat training pictures is from the web and the dev/test pictures are from users cell phone they will mismatch. What is L2-regularization actually doing? Each of C values in the output layer will contain a probability of the example to belong to each of the classes. So it's as if on every iteration you're working with a smaller NN, and so using a smaller NN seems like it should have a regularizing effect. If we just throw all the data we have at the network during training, we will have no idea if it has over-fitted on the training data. Then after your model is ready you try and evaluate the testing set. In this post, I will be explaining various terminologies and methods related to improving the neural networks. Since the risk is a very non-convex function of w, the nal vector w^ of weights typically only achieves a local minimum. This algorithm speeds up the gradient descent. If we have data like the temperature of day through the year it could be like this: This data is small in winter and big in summer. 5 stars. The shape of the cost function will be consistent (look more symmetric like circle in 2D example) and we can use a larger learning rate alpha - the optimization will be faster. It could contain some ups and downs but generally it has to go down (unlike the batch gradient descent where cost function descreases on each iteration). We do this because we want the neural network to generalise well. It's intended for normalization of hidden units, activations and therefore speeding up learning. In the older days before deep learning, there was a "Bias/variance tradeoff". Momentum helps the cost function to go to the minimum point in a more fast and consistent way. If we plot this data we will find it some noisy. The initialization in this video is called "He Initialization / Xavier Initialization" and has been published in 2015 paper. Recently Microsoft trained 152 layers (ResNet)! You can always update your selection by clicking Cookie Preferences at the bottom of the page. Improving Generalization for Convolutional Neural Networks Carlo Tomasi October 26, 2020 Stochastic Gradient Descent (SGD) minimizes the training risk L T(w) of neural network hover the set of all possible network parameters in w 2Rm. Making the NN learn the distribution of the outputs.

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